What would be the problem if my wipers work in only one speed, and get stuck?

The wiper motor is on the way out. Replace it ASAP. When it goes I guarantee it will be raining.

I replaced the motor and still did the same, so changed the little transmission and did the same.. So last thing would be the switch?? Right

My first inclination was the switch. The electric motor speed runs on the amount of less resistance put on the electrical load coming into the motor itself. If it runs under a more resistive load, it should run when the switch is moved to allow more amps into the motor. So the motor should be good. The transmission, if it runs freely, should work at any speed. So the source of power has to go through the switch. Actually it is the easiest to change out and the least expensive fix. As long as you're at it, check the blades and see if you need to spend the $7.50 for new blades also.

I tried the motor and switch replaced both on my 2007 Chevy impala My windshield wipers still not working?